Details

Time bar (total: 12.8s)

sample59.0ms

Algorithm
intervals
Results
17.0ms294×body80valid
13.0ms30×body1280valid
7.0ms31×body640valid
2.0ms11×body320valid
1.0ms5×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
12616
26716
324116
4109716
done500016

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.6b
(* (* x (pow sin 2.0)) x)
7.8b
(* x (pow sin 2.0))
19.7b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
122×add-exp-log
82×prod-exp
34×add-cbrt-cube
18×pow-to-exp pow-exp
17×add-sqr-sqrt
16×div-exp cbrt-unprod
12×add-cube-cbrt *-un-lft-identity
11×associate-*r* associate-*l*
7×unpow-prod-down
6×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 123
Calls
4 calls:
64.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
23.0ms
(* (* x (pow sin 2.0)) x)
14.0ms
(* x (pow sin 2.0))
66.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series882.0ms

Counts
4 → 12
Calls
4 calls:
319.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
156.0ms
(* (* x (pow sin 2.0)) x)
140.0ms
(* x (pow sin 2.0))
266.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify853.0ms

Counts
135 → 135
Iterations

Useful iterations: 2 (241.0ms)

IterNodesCost
01792045
14211897
214451617
done50001617

prune308.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.6b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
19.7b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite535.0ms

Algorithm
rewrite-expression-head
Rules
416×add-exp-log
343×prod-exp
84×pow-to-exp pow-exp
52×add-cbrt-cube
43×div-exp
29×cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
9×associate-*l*
6×pow1 unpow-prod-down
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 194
Calls
4 calls:
30.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
201.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
80.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
211.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series929.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
331.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
161.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
288.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.0s

Counts
206 → 206
Iterations

Useful iterations: done (995.0ms)

IterNodesCost
02115143
15453013
221092569
done50002565

prune299.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
19.7b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
466×add-exp-log
382×prod-exp
90×pow-to-exp pow-exp
58×add-cbrt-cube
52×div-exp
34×cbrt-unprod
8×associate-*l*
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-undiv
5×pow1
3×expm1-log1p-u unpow-prod-down times-frac log1p-expm1-u associate-/l* add-log-exp
2×associate-*r* *-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv sqr-pow
Counts
3 → 184
Calls
3 calls:
41.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
101.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
107.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series772.0ms

Counts
3 → 9
Calls
3 calls:
159.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
327.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
285.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify857.0ms

Counts
193 → 193
Iterations

Useful iterations: 2 (288.0ms)

IterNodesCost
01885240
14803102
218642616
done50002616

prune220.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
6.1b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
15.6b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
455×add-exp-log
371×prod-exp
89×pow-to-exp pow-exp
58×add-cbrt-cube
53×div-exp
33×cbrt-unprod
8×associate-*l*
7×cbrt-undiv add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1
3×expm1-log1p-u unpow-prod-down times-frac log1p-expm1-u associate-/l* add-log-exp
2×associate-*r* *-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv sqr-pow
Counts
3 → 182
Calls
3 calls:
85.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
86.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
29.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series838.0ms

Counts
3 → 9
Calls
3 calls:
321.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
287.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
230.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify883.0ms

Counts
191 → 191
Iterations

Useful iterations: 2 (307.0ms)

IterNodesCost
01915082
15103288
219102764
done50002764

prune204.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

regimes275.0ms

Accuracy

0% (1.7b remaining)

Error of 7.1b against oracle of 5.4b and baseline of 7.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01632
12032
done2032

end0.0ms

sample1.6s

Algorithm
intervals
Results
549.0ms9090×body80valid
272.0ms785×body1280valid
239.0ms997×body640valid
94.0ms557×body320valid
37.0ms308×body160valid